Here's a graph showing the female labor force participation rate for high-income countries on the horizontal axis, and the fertility rate on the vertical axis. The best-fit line clearly shows that countries where women are more likely to be in the labor force are also countries with higher fertility rates.

The details of this evidence are interesting. Traditionally, if one looks at data from within a single country, a typical finding was that women who had more children were indeed less likely to be in the labor force during their lifetimes. But in high-income countries, that relationship now appears to have changed. Kinoshita and Kochhar explain (citations omitted):

Researchers have explained this apparent contradiction by looking at the contribution that men make to their households. They find that women in countries where men participate more in housework and child care are better able to combine motherhood and a job, which leads to greater participation in the labor force at relatively high fertility levels.

Moreover, the relationship between female labor participation and fertility seems to have shifted from negative to positive in Organisation for Economic Co-operation and Development advanced economies since 1985. This shift implies that when more women work and bring home a paycheck households can support more children. This trend also reflects changes in social attitudes toward working mothers, fathers’ involvement in child care, and advances in technology that allow more workplace flexibility. Public policies such as more generous parental leave and greater availability of child care also helped.

My own unscientific explanation for this change, vetted mainly by my wife and some female friends, is that women in societies with more traditional gender roles may not have the freedom to get the level of skills and jobs they want in the paid labor market, but they recognize that having children could lock them into a very traditional lifestyle that they do not want. When a society breaks out of those traditional gender roles, women both have greater opportunities in the labor market and also greater time-and-energy support from their spouse within the family, at which point having children looks like a more attractive life choice.